A jogger on a circular track that has a radius of .250 km runs a distance of 1 km. What angular distance does the jogger cover in a) radians and b) degrees?
A great explanation would be very wonderful! Thanks!
2007-11-29 12:12:45 · 5 answers · asked by bee_rice33 1 in Science & Mathematics ➔ Physics
Okay, well if the track has a radius of .25 km, you need to find the circumference first by multiplying that by 2pi:
C = (2)(radius)(pi)
Then, should 1 km, or the total distance the runner has traveled around the circular track, and divide it by C. This will give you the number of times he has gone around. Don't be surprised if it's not an integer - the decimals are fine. We'll call this number "x".
If you multiply x by 360 (the number of degrees in a circle), you'll get the angular distance in degrees.
To get the answer to a, multiply the angular distance in degrees by pi over 180 (pi/180). This is the conversion factor between degrees and radians, and if you cancel, you'll angular distance in radians.
It's that simple...good luck with your calculations!
2007-11-29 12:22:39 · answer #1 · answered by Tunesmith 3 · 0⤊ 0⤋
The radius is .250 km and the diameter is thus 0.5 km. Multiply this by pi and you have the circumference, which is approx 1.57 km. The jogger has run 1/1.57 = 0.637 of the way around the track. There are 360 degrees in the circle, so the runner has covered 0.637*360 = 229.3 degrees. There are 2 pi radians in a full circle so the runner has covered 0.637*2pi = 4 radians.
2007-11-29 20:22:45 · answer #2 · answered by KeplJoey 7 · 0⤊ 0⤋
The diameter of the track is:
D = 2*pi*r = 2*pi*(0.25 km) = 1/2*pi km = 1.57 km
Now a circle has 360 degrees or 2*pi radians of angle. Since teh runner goes 1 km the angular distance is:
1km/(1.57 km)*360 deg = 229.2 deg
1 km/(1.57 km)*2*pi radians = 4 radians
2007-11-29 20:21:03 · answer #3 · answered by nyphdinmd 7 · 0⤊ 0⤋
Once around the track or 360 DEG is equal to TWO PI RADIANS. So one radian equals 360/(2 X 3.14)= 57.32 DEG.
2007-11-29 20:20:12 · answer #4 · answered by jimmymae2000 7 · 0⤊ 0⤋
The arc length s and angle θ in radian are connected by the formula
θ = s/r = [1km] / [0.25 km] = 4 radian.
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Ï radian is equal to 180 degree.
4 radian = [180 / Ï] *4 = 229.18°
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2007-11-29 21:20:53 · answer #5 · answered by Pearlsawme 7 · 0⤊ 0⤋